Tracking using field mapping

ABSTRACT

Methods and systems for determining the position of an object, such as tracking the position of one or more catheters in a patient&#39;s heart cavity are disclosed herein.

TECHNICAL FIELD

This invention relates to determining the position of an object, such astracking the position of one or more catheters in a patient's heartcavity.

BACKGROUND

Use of minimally invasive procedures, such as catheter ablation, totreat a variety of heart conditions, such as supraventricular andventricular arrhythmias, is becoming increasingly more prevalent. Suchprocedures involve the mapping of electrical activity in the heart(e.g., based on cardiac signals), such as at various locations on theendocardium surface (“cardiac mapping”), to identify the site of originof the arrhythmia followed by a targeted ablation of the site. Toperform such cardiac mapping a catheter with one or more electrodes canbe inserted into the patient's heart chamber.

Under some circumstances, the location of the catheter in the heartchamber is determined using a tracking system. Catheter tracking is acore functionality of modern mapping systems that also include softwareand graphic user interface to project electrical data on 3D renderingsof cardiac chambers. Currently there are several tracking systemsavailable, some more useful and commonly used than others. Some systemsare based on the use of magnetic or electric fields from externalsources to sense and track the location of the catheter. Some are basedon the use of magnetic or electric fields sources mounted on the trackedcatheters.

SUMMARY

In some aspects, a method includes causing current to flow amongmultiple current injecting electrodes, at least some of the currentinjecting electrodes being placed in stable locations inside a patient'sbody to generate a field in an organ. The method also includes, inresponse to the current flow caused by the current injecting electrodes,measuring a signal at each of multiple measuring electrodes on acatheter for each of multiple locations of the catheter. The method alsoincludes determining expected signals at additional locations within theorgan based on the measured signals and determining a position of atleast one of the measuring electrodes of the catheter and/or a measuringelectrode of another catheter in the organ based on at least theexpected signals.

Embodiments can include one or more of the following.

The current injecting electrodes are not on the catheter that includesthe measuring electrodes.

Determining the expected signals can include determining expectedsignals in the absence of information from an external tracking system.

Determining the expected signals can include determining relativelocations of the plurality of measuring electrodes at different ones ofthe multiple locations in the organ based on the measured signals.

Determining the relative locations can include reconciling fieldsmeasured at the different ones of the multiple locations.

Reconciling the fields can include using a cost minimization function onone or more of a point, multiple points, a surface, and a volume.

Determining the relative locations can include determining a translationand rotation between the plurality of measuring electrodes at themultiple locations.

The measured signals for the catheter at each location can define acorresponding set of measurements and determining the expected signalscan include combining information from the different sets to determine afield map indicative of the expected signals at the additionallocations.

Combining can include aligning the information from the different setsto account for the different locations of the catheter based on theknown relative locations of the measuring electrodes on the catheter.

The information from each of the sets of measurements can be a localfield map.

Determining the expected signals can include reconciling the local fieldmaps from the multiple locations.

Reconciling the local field maps can include using a cost minimizationfunction on one or more of a point, a surface, and a volume.

Reconciling the local field maps can include determining a translationand rotation between the plurality of the local field maps.

Determining the expected signals can include determining the expectedsignals based on the measured signals and known relative locationsbetween the multiple measuring electrodes on the catheter.

The expected signals can be a field map.

The field map can be a differentiable function.

Determining the expected signals can include using Laplace's equation,Poisson's equation, and/or a polynomial estimation.

The current injecting electrodes can be mounted on one or more cathetersthat are secured inside the organ.

The current injecting electrodes can include both electrodes mounted onone or more catheters secured inside the organ and one or morebody-surface electrodes.

Measuring the signal can include measuring potentials.

Measuring the signal at the multiple locations can include moving thecatheter to the multiple locations within the organ, and using themeasuring electrodes to measure signals for each of the multiplelocations of the catheter.

Determining expected signals can include for the multiple locations,modeling portions of the field using the measured signals from the oneor more measuring electrodes to generate multiple models of portions ofthe field and combining the multiple models to generate a combined fieldmodel.

Combining the multiple models can include sequentially combining themultiple models to generate the combined model of the field.

Combining the multiple models can include concurrently combining themultiple models to generate the combined model of the field.

The combined field model can include a weighted mean of the multiplemodels of the portions of the field.

The method can also include removing the measuring electrodes from theorgan and subsequent to removing the measuring electrodes from the organusing the expected signal measurements to track a location of themeasuring electrode of the another catheter.

The current-injecting electrodes can include at least three sets ofcurrent injecting electrodes, and wherein the causing of the currentflow includes causing current to flow between each set of currentinjecting electrodes.

The organ can be the patient's heart.

Determining the position can include determining the position of themeasuring electrode of the another catheter with the another catheterbeing a separate catheter from the catheter that includes the multiplemeasuring electrodes.

The measured signals and expected signals can be processed to accountfor respiration and heart beat.

Processing the measured signals and expected signals can include usinginformation from a catheter electrode positioned in a stable locationrelative to the organ.

The stable location can be the coronary sinus.

In some additional aspects, a system includes a catheter configured forinsertion into an organ in a patient's body and includes multiplemeasuring electrodes. The system also includes multiple currentinjecting electrodes placed in stable locations inside a patient's bodyto generate a field in an organ. The system also includes an electroniccontrol system coupled to the multiple current injecting electrodes andto the measuring electrodes. The electronic control system is configuredto cause current to flow among multiple current injecting electrodes togenerate a field in an organ and to measure the field and, in responseto the current flow caused by the current injecting electrodes, measurea signal at each of the multiple measuring electrodes for each ofmultiple locations of the catheter. The system also includes aprocessing system coupled to the electronic system. The processingsystem is configured to determine expected signals at additionallocations within the organ based on the measured signals and determine aposition of at least one of the measuring electrodes of the catheterand/or a measuring electrode of another catheter in the organ based onat least the expected signals.

Embodiments can include one or more of the following.

The current injecting electrodes can be mounted on one or more cathetersthat are secured inside the organ.

The measuring electrodes mounted on the catheter can include electrodesthat can be moved and positioned at multiple locations in an organ.

The current-injecting electrodes can include at least three sets ofcurrent injecting electrodes.

The current injecting electrodes are not on the catheter that includesthe measuring electrodes.

The processing system can be further configured to determine theexpected signals in the absence of information from an external trackingsystem.

The processing system can be further configured to determine relativelocations of the plurality of measuring electrodes at different ones ofthe multiple locations in the organ based on the measured signals.

The processing system can be further configured to reconcile fieldsmeasured at the different ones of the multiple locations using a costminimization function.

The processing system can be further configured to determine atranslation and rotation between the plurality of measuring electrodesat the multiple locations.

The measured signals for the catheter at each location define acorresponding set of measurements and the processing system can befurther configured determine the expected signals by combininginformation from the different sets to determine a field map indicativeof the expected signals at the additional locations.

The processing system can be further configured to combine theinformation from the different sets to determine a field map by aligningthe information from the different sets to account for the differentlocations of the catheter based on the known relative locations of themeasuring electrodes on the catheter.

The expected signals can be a field map.

The processing system can be further configured to determine theexpected signals using Laplace's equation, Poisson's equation, and/or apolynomial estimation.

The current injecting electrodes can include both electrodes mounted onone or more catheters secured inside the organ and one or morebody-surface electrodes.

The processing system can be further configured to use the expectedsignal measurements to track a location of the measuring electrode ofthe another catheter.

The processing system can be further configured to process the measuredsignals and expected signals to account for respiration and heart beat.

In some additional aspects, a method includes generating a baselinesignal measurement by causing current to flow among multiple currentinjecting electrodes at least some of the current injecting electrodesbeing placed in stable locations inside a patient's body to generate afield in an organ and in response to the current flow, measuring asignal at one or more measuring electrodes positioned at one or moresecure locations. The method also includes subsequent to generating thebaseline signal measurement, causing current to flow among the multiplecurrent injecting electrodes, in response to the current flow, measuringa signal at the one or more measuring electrodes, and comparing themeasured signal to the baseline signal to generate a comparison result.

Embodiments can include one or more of the following.

The method can also include determining whether a location of themultiple current injecting electrodes inside the patient's body haschanged based on the comparison result.

The method can also include providing an audio or visual indicator upondetermining that the location of the multiple current injectingelectrodes has changed.

The one or more measuring electrodes can be one or more ECG leads.

The one or more measuring electrodes can be one or more body surfaceelectrodes.

The method can also include, subsequent to generating the baselinesignal measurement, in response to the current flow, measuring a signalat each of multiple measuring electrodes on a catheter for each ofmultiple locations of the catheter and determining expected signals forthe measuring electrodes at additional locations within the organ basedon the measured signals.

The method can also include, subsequent to generating the baselinesignal measurement, in response to the current flow, measuring a signalat each of multiple measuring electrodes on a catheter and determining arelative location of the catheter based on the signals measured by themultiple measuring electrodes on the catheter.

The one or more measuring electrodes can include one or more stableintracardiac electrodes.

The organ can be a patient's heart.

Generating the baseline signal measurement can include compensating forrespiration and heartbeat of the patient.

Comparing the measured field to the baseline signal can includecalculating a residual norm between the baseline signal and the measuredsignal.

Comparing the measured field to the baseline signal can includecomparing the residual norm to a threshold value.

The method can also include providing information to enable a clinicianto guide the current injecting electrodes to a location where thebaseline signal measurement was generated.

Comparing the measured field to the baseline signal can includecalculating a displacement trajectory.

The displacement trajectory can provide a three-dimensional modelproviding an indication of a current location of the current injectingelectrodes and an indication of the location where the baseline signalmeasurement was generated.

In some aspects, a system includes one or more measuring electrodespositioned at one or more secure locations and multiple currentinjecting electrodes at least some of the current injecting electrodesbeing placed in stable locations inside a patient's body to generate afield in an organ. The system also includes an electronic control systemcoupled to the multiple current injecting electrodes and to the one ormore measuring electrodes. The electronic control system is configuredto cause current to flow among multiple current injecting electrodesand, in response to the current flow, measure a signal at the one ormore measuring electrodes. The system also includes a processing systemcoupled to the electronic system. The processing system is configured togenerate a baseline signal measurement, subsequent to generation of thebaseline signal measurement, compare a measured signal from the one ormore measuring electrodes to the baseline signal to generate acomparison result, and determine whether a location of the multiplecurrent injecting electrodes inside the patient's body has changed basedon the comparison result.

Embodiments can include one or more of the following.

The system can also include an indicator configured to provide an audioor visual indication upon determining that the location of the multiplecurrent injecting electrodes has changed.

The one or more measuring electrodes can be one or more ECG leads.

The one or more measuring electrodes can be one or more body surfaceelectrodes.

The system can also include multiple measuring electrodes on a catheter.The electronic control system can be further configured to measure asignal at each of multiple measuring electrodes on the catheter for eachof multiple locations of the catheter and the processing system can befurther configured to determine expected signals for the measuringelectrodes at additional locations within the organ based on themeasured signals.

The processing system can be further configured to determine a relativelocation of another catheter based on the signals measured by themultiple measuring electrodes on the catheter.

The one or more measuring electrodes can be one or more stableintracardiac electrodes.

The processing system can be further configured to compensate forrespiration and heartbeat.

The processing system can be further configured to compare the measuredfield to the baseline signal using a residual norm between the baselinesignal and the measured signal.

The processing system can be further configured to compare the measuredfield to the baseline signal by comparing the residual norm to athreshold value.

The system can also include a display unit configured to provideinformation to enable a clinician to guide the current injectingelectrodes to a location where the baseline signal measurement wasgenerated.

The system can also include a display unit configured to display adisplacement trajectory.

The displacement trajectory can provide a three-dimensional modelproviding an indication of a current location of the current injectingelectrodes and an indication of the location where the baseline signalmeasurement was generated.

Embodiments of the systems and methods described herein may also includedevices, software, components, and/or systems to perform any featuresdescribed above in connection with methods and systems described herein.

Embodiments of the methods and systems generally disclosed herein can beapplied to determining the position of any object within an organ in apatient's body such as the patient's heart, lungs, brain, or liver.

As used herein, the “position” of an object means information about oneor more of the 6 degrees of freedom that completely define the locationand orientation of a three-dimensional object in a three-dimensionalcoordinate system. For example, the position of the object can include:three independent values indicative of the coordinates of a point of theobject in a Cartesian coordinate system and three independent valuesindicative of the angles for the orientation of the object about each ofthe Cartesian axes; or any subset of such values.

As used herein, “heart cavity” means the heart and surrounding tissue.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. In case of conflict withdocuments incorporated herein by reference, the present documentcontrols.

The details of one or more embodiments of the invention are set forth inthe accompanying drawings and the description below. Other features,objects, and advantages of the invention will be apparent from thedescription and drawings, and from the claims.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exemplary schematic diagram of an arrangement forpositioning current injection electrodes (CIE) and potential measuringelectrodes (PME) with respect to a patient's heart cavity.

FIGS. 2A, 2B, and 2C are diagrams of exemplary fields generated bymultiple CIE configurations and measured by a field mapping catheter(FMC).

FIGS. 3A, 3B, and 3C are exemplary fields generated by multiple CIEconfigurations and measured by a potential measuring electrode (PME).

FIG. 4 is a schematic representation of the field mapping system

FIGS. 5A, 5B, and 5C are exemplary field diagrams.

FIGS. 6A, 6B, and 6C are exemplary local field models associated withthe fields shown in FIGS. 5A, 5B, and 5B.

FIGS. 7A, 7B, 7C, and 7D are exemplary field models.

FIG. 8 is an exemplary field map.

FIG. 9 is a diagram of an exemplary volume and an enclosing surfacesurrounding a field mapping catheter.

FIG. 10 is a flow chart of a method for generating a field map for anenclosed volume.

FIG. 11 is an exemplary flow chart for determining positions ofelectrodes using a field map.

FIG. 12 is a table that includes contour plots of two-dimensional slicesof the local model and global field map.

FIG. 13 is a diagram of three-dimensional tracked PME locations.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

Embodiments disclosed herein include a method and system for generatinga model of the field that provides expected signal measurements of thefield at various locations within the heart cavity and determining theposition of a catheter in a patient's heart cavity using the determinedmodel of the field.

More particularly, the methods and systems described herein provide amethod for tracking electrodes mounted on catheters within and relativeto the cardiac cavity, including any number of chambers within thiscavity and the blood vessels surrounding it, but it can be used fortracking catheters in other body organs as well. Electrodes can bemounted on one or multiple catheters and by tracking these electrodesthe location of such catheters can be determined and the catheters canbe tracked. By knowing the physical characteristics of a catheter andthe position of the electrodes on it, it is possible to track specificportions of the catheter (e.g. the distal section) or to determine theshape and the orientation of the catheter (e.g. by using a splinefitting method on the location of multiple electrodes of the samecatheter). Electrodes can also be mounted on other devices that requiretracking inside the heart cavity.

In some examples, the system tracks the location of the electrodes andcatheters by generating a multitude of fields using field generatingdevices (FGD) positioned and secured in stable locations internally(e.g., field generating devices secured in the coronary sinus, atrialappendage, and/or apex) or externally (e.g., field generating devicessecured on back, chest, or other body surface) and using measurements ofthe same fields on electrodes mounted on other catheters to locate them.In general, a FGD can be an element or device which can create ameasurable field of some type, e.g., potential, magnetic, acoustic, etc.One implementation of the system uses current injecting electrodes (CIE)to create potential fields and uses potential measuring electrodes (PME)to measure the fields. In general, a CIE can be an element whichgenerates a potential field by injecting current into the area ofinterest, a CIE is paired with an element providing a sink for thecurrent, and a PME can be an electrode which can measure a potentialfield. However, the methods and approaches described herein can beapplied to systems and methods using magnetic fields, acoustic fields,or other measurable fields.

The disclosed invention does not require but may use any externalpatches attached to the body, or any other external energy emitter.However, the invention works even if only internal field generators areavailable, and it does not require any knowledge about the location inspace of any field generator. In some embodiments, field generation mayuse objects that are secured to the heart itself, reducing inaccuraciesfrom motion artifacts that are experienced by systems that arereferenced to an external coordinate system or are affected by relativemotion between the field generator and the heart (e.g. skin to heart).The system also incorporates methods for detecting when the fieldgenerators have altered location and for guiding the user inrepositioning them.

In general, in one aspect, a catheter that includes one or morepotential measuring electrodes (PME) that can measure the fields (e.g.,measure potentials in the heart cavity in response to the currentprovided by the CIEs) is used for generating a field map. The field mapprovides expected signal measurements of the field at various locationswithin the heart cavity. In some embodiments, it is not necessary forthe field mapping catheter to be tracked by an independent trackingsystem.

Once a field map is generated, the catheter used to generate the fieldmap can optionally be taken out of the body. However, the CIE used togenerate the fields are left in their stable locations for subsequentuse in tracking other electrodes. Using the field map it is possible todetermine the location of any potential measuring electrodes (PME) thatcan measure the generated fields (e.g., the fields generated using thecurrent injecting electrodes) inside the volume covered by the fieldmap. The position of a tracked PME is determined by comparing themeasured field value and the modeled field values. The position in thefield map that holds a value matching the measurement of the tracked PMEis assigned as the location of that PME.

In the above discussion and in the details that follow, the focus is ondetermining the position of one or more catheters in a heart cavity fordiagnosis and treatment of cardiac arrhythmias. However, this is only anexemplary application. The method and system generally disclosed hereincould be used to track essentially any catheter mounted with at leastone electrode, regardless of the catheter's intended function. Relevantexamples include endocardial biopsies, therapies involvingintra-myocardial injections of cells, drugs, or growth factors, and thepercutaneous placement cardiac valves. In other examples, the method andsystems generally disclosed herein can be applied to determining theposition of any object within any distribution of materialscharacterized by a conductivity profile. For example, the methods andsystems generally disclosed herein can be applied to determining theposition of any object within an organ in a patient's body such as thepatient's heart, lungs, brain, or liver.

FIG. 1 shows an exemplary schematic diagram of an arrangement forpositioning current injection electrodes (CIE) and a field mappingcatheter with respect to a patient's heart cavity. It shows three CIEpairs (e.g., CIE¹⁻-CIE¹⁻; CIE₂₊-CIE²⁻; and CIE₃₊-CIE³⁻) mounted onelectrodes on a single catheter placed in the coronary sinus, which actas field generating devices. As described herein, while shown aspositioned in the coronary sinus, other locations outside of the heartchamber, within the organ itself, and/or outside of the patient's bodycould be used to secure the CIE pairs.

A field mapping catheter (FMC) is placed within the cardiac chamber andcan move relative to the cardiac chamber. One exemplary FMC is acatheter with at least four non-planar field measuring sensors. The FMCis able to measure the fields generated by the different CIE pairs. Thespatially diverse field measurements allow the field in the regionaround the catheter to be modeled and predicted. FIG. 1 shows multiplelocations of the FMC (e.g., Field mapping catheter positions 1 . . . n)as the FMC moves through a cardiac chamber and measures the fieldsacross different locations.

Field mapping is performed in order to generate a completerepresentation of the fields within which electrodes and catheters canbe tracked. Field mapping involves the collection of measurements of thefields generated by the FGD at one or more distinct times and across oneor more distinct locations. The measurements are collected by one ormore field mapping catheters (FMC). The FMC measurements are combinedwith information about relative FMC locations to create the field mapthat is used for tracking electrodes and catheters.

If the FMC contains four or more electrodes not entirely contained in aplane, its measurements can be used to generate a local field model,that is, an estimate of the potential measurements in the volumesurrounding the FMC for each of the fields generated by the FGD.

As shown in FIGS. 2A-2C, for a particular location of the FMC, the FGDgenerate multiple fields (e.g., by using different ones of the CIE pairsCIE₁₊-CIE¹⁻; CIE₂₊-CIE²⁻; and CIE₃₊-CIE³⁻), each of which can be modeledin a region surrounding the FMC. Local field models (e.g., local modelsof expected signal measurements in a region surrounding the FMC) made atmultiple different locations of the FMC can then be combined into thefield maps (e.g., expected signal measurements of the field at variouslocations within the heart cavity) required by the tracking system. Themodel of the field can be determined, for example, by solving Laplace'sequation in a homogeneous medium representing the cardiac chamber togenerate the local field models or the field map. In some additionalexamples, the model of the field can be determined using othermathematical methods for characterizing the fields, e.g., interpolationand extrapolation of measured values or fitting to a parametric model.The combination of techniques can be used to generate a field map thatis accurate in areas that are not specifically probed by the FMC andeven in areas not lying between positions that were probed.

In order to combine individual FMC measurements (e.g., measurementscollected at different positions within the organ) to generate the fieldmap, the relative locations at which the measurements were collected areused. One method of determining FMC locations is by using an independenttracking system. Such systems are known in the art and may use magneticor acoustics fields to determine location of a sensor, such as themethod disclosed, for example, in U.S. patent application Ser. No.12/258,688 entitled “TRACKING SYSTEM USING FIELD MAPPING” and filed Oct.27, 2008, the contents of which is incorporated by reference herein. Incontrast to methods using an independent tracking system, methods ofdetermining relative FMC locations described herein involve reconcilingthe local field models corresponding to the FMC measurements.Reconciling two or more local field models may involve minimizing a costfunction on a point, surface, volume or combination of these within theintersection of volumes described by the separate models. Modelreconciliation can also make use of a priori information about theexpected characteristics of the field or the shape of the FMC.

The field map can be generated using the FMC measurements and theirrelative locations. The field map can be a weighted mean of the localfield models such that the local field models from the nearest FMCpositions have the greatest impact on the field map. Another option isto generate the field map using all of the FMC electrode locations andmeasurements in a method analogous to how a local field model isgenerated. The complete set of locations can be used to solve theinverse Laplace problem, or mathematical methods may be used tointerpolate the measurements or fit them to a parametric model.

In general, the field map generated can be represented by adifferentiable function. The tracking algorithm, which matches anelectrode's measurements with a location in the field map, requiresfinding a minimum in a cost function using optimization. Optimizationtechniques of differentiable functions are faster and more accurate thanother techniques, giving another advantage to the disclosed invention.

Once a sufficiently accurate and complete field map is generated, theFMC can be removed from the body. This may be advantageous when it isdesired to have fewer catheters inside the body organ for clinicalreasons. Alternatively, the FMC may remain in the body while one or moreother catheters are tracked based on the field map generated using theFMC.

Using the field map, it is possible to determine the location of any PMEthat can measure the generated fields inside the volume covered by thefield map.

FIGS. 3A-3C show an exemplary PME exposed to the three fields of theschematic system (e.g., the fields generated by the three differentpairs of CIE). Using the field map of the same fields, the trackingprocessor can identify the unique position in the chamber which wouldcause the PME to measure the three observed potentials. The trackingprocessor may improve tracking performance by incorporating any a prioriinformation about a catheter, e.g., catheter geometry (e.g. electrodedimensions and inter-electrode distance) or catheter dynamics (e.g.material properties or known shapes).

Using the field map, the system can track sensors inside a body withouthaving these sensors emit any field that needs to be detected. That is,the CIE used to generate the field are active, while the tracked PME arepassive. In contrast, systems that require the tracked electrode to beactive often track a single electrode at any given time. For thetracking of multiple electrodes, such systems usually activate oneelectrode at a time and sequentially cycle through all trackedelectrodes. Since there is a minimum duration that each electrode needsto be active in such a system, and there is also a desired refreshingrate for the tracked location, there is a limit to the number ofelectrodes that can be tracked simultaneously in such systems. Due tothe passive nature of the tracked PME in the systems and methodsdescribed herein, there is no limit to the number of PMEs that can betracked simultaneously.

Additionally, in some aspects, the systems and methods described hereinprovide a method to monitor the location stability of the FGD usingcutaneous patches (e.g., ECG leads) and intracardiac electrodes. In casethe FGD is displaced, the system can enable the clinician to repositionthe FGD appropriately.

Field Generation and Measurement

Referring back to FIG. 1, FIG. 1 shows an exemplary schematic diagram ofan arrangement for positioning multiple current injection electrodes(CIE) mounted on one or more catheters. The CIE are located in a stableposition in the heart and are secured in a way that minimizes relativemovement between the electrodes and the heart walls. This can be doneeither by choosing a location such that the catheter will conform to theanatomy and will stay in a fixed position (e.g., coronary sinus,appendage or apex), or by using a fixation mechanism (e.g. screw-in leador balloon mechanism).

In general, in order to inject current an electrode must have impedancethat is low enough for the current driver to overcome (e.g. 5 kΩ). Lowimpedance can be achieved by a sufficient surface area or by usingmaterials or coatings that lower the impedance of the electrode. Itshould be noted that any sufficiently low impedance electrode can beused for current injection, and in a case where many or all electrodeson a certain catheter are capable of injecting current, the designationof such electrodes as CIE only indicates that these electrodes areactually being used for current injection.

In some embodiments, for example, as shown in FIG. 1, a set of 3 CIEconfigurations can be arranged to span three dimensional (3D) space andprovide XYZ coordinates of other electrodes. Because the conductivity ofthe heart is inhomogeneous and varies across frequency, it is alsopossible to create a potential field with sufficient spatial diversityusing fewer CIE configurations. An example of a CIE configuration is apair of CIE configured as a dipole, having one CIE acting as a currentsource and the other CIE acting as a current sink. An electrode can beused in more than one CIE configuration. Ideally, the electrodes are notall placed in the same plane so that a 3D space is clearly spanned. Forthis reason, in some embodiments, a minimum of 4 CIE configurations canbe preferable.

Other configurations of CIE are possible as long as these configurationsspan the 3D space. Examples of such a configuration could be quadruplesinvolving 4 CIE, or even a non-symmetric configuration involving 3 CIE.CIE can be on the same catheter or on different catheters. They can bein the same chamber, in different chambers, in the cardiovascular systemsurrounding the heart or in other tissue. It is also possible toconfigure CIE such that current is sourced by intracardiac electrodeswhile a cutaneous patch acts as a sink. It should be understood that thedistinction between source and sink is of no significance, in particularwhen the signal is modulated by a carrier frequency. For simplicity, amethod using electrode pairs will be explained herein, but the samemethod can be applied using other configurations. In such cases there isa need for the electrode configurations to create a set of fields withsufficient spatial variety to uniquely locate the set of electrodesbeing tracked.

It should be appreciated that knowing the spatial configuration of CIEsis not required for the tracking system to operate as long as the pairsused for injecting the currents span the three-dimensional space of thechamber as described. The properties of the medium and the inhomogeneityof it are not modeled in any way, and no prior knowledge is requiredabout the medium.

Pending patent application Ser. No. 12/061,297 entitled “IntracardiacTracking System” and filed Apr. 2, 2008, whose disclosure isincorporated herein in its entirety by reference, describes an exemplarysignal acquisition and generation module.

In the tracking system described herein, potential measuring electrodes(PMEs) mounted on tracked catheters measure both potentials from cardiacactivation and the fields generated by the CIE. There is a need toseparate the tracking signal being used for location determination fromthe cardiac signal being used for generating electrical activation maps.The CIE inject current at a frequency higher than cardiac activation(cardiac activation <2 kHz, CIE>4 kHz, e.g. 5 kHz) such that the twotypes of signals can be easily distinguished using frequency analysis.It should be noted that other methods for distinguishing between the CIEsignal and the cardiac activation signal can be used, such as injectinga spread-spectrum signal having a low energy level in the frequencyrange of the cardiac activation signal, and detecting thisspread-spectrum signal in the signal collected by the all PME.

In order to span the space, multiple CIE configurations must injectcurrent (e.g. three pairs not residing in the same plane). There is aneed to determine the source of the injected signal and to trace it to aspecific CIE configuration. One implementation requires the pairs of CIEto inject current sequentially, one pair at a time, so that it ispossible to trace the source of the measured PME signals to a specificpair. This is called time-division multiplexing. In the case oftime-division multiplexing, CIE are activated in sequence such that atone point in time one pair is activated (e.g. CEI₁₊ and CEI¹⁻) and atthe next point in time another pair is activated (e.g. CIE₂₊ and CIE²⁻).The switching between pairs may occur every cycle (e.g. ⅕ kHz=200 μs) orevery few cycles (e.g. 20 cycles, 20×200 μs=4 ms). It should be notedthat frequency- or code-division (spread-spectrum) multiplexing, ratherthan time-division, may be used to separate the signals. In the case offrequency-division multiplexing, all CIE pairs may inject the current atthe same time, but each pair uses a different signal frequency. Thesignal collected at the PME is filtered according to the frequency, andthe signal measured in each frequency is then associated with theappropriate originating pair.

The relative impedance between blood and surrounding media varies overfrequency. As a result, injecting current at the same CIE at multiplefrequencies (e.g. 5 kHz and 30 kHz) results in different fields in themedium. This method can be used to diversify the fields obtained withthe same electrodes. This is advantageous when trying to minimize thenumber and span of CIE.

While in some of the specific embodiments that follow the signalsmeasured by the electrodes correspond to the relative strength (e.g.,amplitude) of the measured electrical signal (e.g., potential), furtherembodiments may also analyze the phase of the measured signal, eitheralone or in combination with the amplitude of the measured signal. Thephase of the measured signal is indicative of spatial variations in theimaginary part of the complex conductivity (e.g., permittivity) in thedistribution of materials.

Field Mapping

In general, the system generates a set of expected signals based on thesignals measured by the FMC. One example of a set of expected signals isa field map. A field map assigns scalar or vector measurements of thegenerated fields to positions in the volume within which electrodes andcatheters will be tracked. The field map can be represented as afunction, e.g., a differentiable function. In embodiments in which theabsolute location of the FMC within the organ is not known, a locationof the FMC in the initial measurement may define the origin andorientation of the coordinate frame for the field map. In general, afield is any measurable phenomenon that associates a scalar or vectorvalue to points in space (e.g., to every point in space). PME canmeasure different kinds of scalar fields, such as electrical potentialfield (potential difference relative to a reference location), impedancefield (impedance between every location and a reference location), etc.

The field mapping process uses a catheter that has at least fournon-coplanar PMEs that can measure the fields generated by the CIE. Anexemplary catheter that can be used for the field mapping process is theMEA catheter described in pending patent application Ser. No. 12/005,975entitled “Non contact mapping catheter” and filed Dec. 28, 1007, whosedisclosure is incorporated herein in its entirety by reference. Thecatheter used is referred to as the field mapping catheter (FMC).

Referring now to FIG. 4, in an embodiment of the field mapping systemusing potential fields, FIG. 4 shows schematically a realization of thefield mapping system. The system includes four electrodes (sourceelectrode #1, source electrode #2, source electrode #3, and sinkelectrode). For clarity, this schematic shows the two-dimensional analogto the proposed field mapping system. A real system would locate thefour CIE so that the CIE are not coplanar. The system also includes afield mapping catheter that includes multiple (e.g., at least four)non-coplanar PMEs.

As shown in FIGS. 5A-5C, in operation, the FMC is initially placedsomewhere within the region of interest (e.g., within the organ). Thesystem causes current to flow among the multiple current injectingelectrodes. For example, in the example shown in FIG. 5A the systemcauses current to flow between source electrode 1 (SE₁) and sinkelectrode (SK), in FIG. 5B the system causes current to flow betweensource electrode 2 (SE₂) and sink electrode (SK), and in FIG. 5C thesystem causes current to flow between source electrode 3 (SE₃) and sinkelectrode (SK). As shown in FIGS. 5A-5C, the field generated by eachpair of electrodes is different based on the relative locations of theelectrodes. In response to the current flow caused by the currentinjecting electrodes, the system measures signal at each of multiplemeasuring electrodes on a FMC. More particularly, the system measuresthe potentials for the field generated by each CIE pair at the distinctlocations of its electrodes. The FMC can subsequently be moved toanother location within the region of interest.

As shown in FIGS. 6A-6C, the signal measurements gathered by themeasuring electrodes on a FMC allow the tracking processing unit tocreate a set of expected signal measurements that describe each field ina region around the FMC (referred to herein as a local field model). Alocal field model can be generated for each of the CIE pairs and foreach location of the FMC. The system combines the multiple models togenerate a combined field model that provides a set of expected signalmeasurements for a larger area of the organ than the area that ismodeled by the local field models. The process for creating the localfield model is described in more detail herein. The local field modelsare generated in the absence of information from an external trackingsystem.

The relative positions of the FMC at different locations can bedetermined based on the signal measurements gathered by the measuringelectrodes on a FMC at the different locations. More particularly, thestructure of each field allows relative FMC positions to be determined.As shown in FIG. 7A, when the FMC is shifted to a new location withinthe organ, the PME on the FMC measure a new set of signals (e.g., a newset of potentials). Based on the newly measured set of signals at thenew location, a second local field model is constructed as shown in FIG.7B. For illustration, the fields generated by source electrode #1 areshown in FIGS. 7A and 7B. Additional fields would be measured andadditional local field models can be constructed based on the signalsmeasured from the fields produced by the other current injectingelectrodes.

The relative location of the FMC can be determined based on the localfield models generated at each of the locations. To locate the secondFMC position relative to the initial position, the system initiallyassumes that it occupies a particular, but likely incorrect, location.When the predictions of the two local field models on the regions ofoverlap are compared, the error in position will result in discrepanciesbetween the predictions. For example, as shown in FIG. 7C, an initialposition is assumed for the second location of the FMC. However, thefield model generated for the second location does not match theprevious model of the field so the FMC is assumed to be in the wronglocation and orientation. This schematically shows how the second fieldmodel, which is tied to the coordinate frame of the FMC, does not matchthe previous model of the field when the FMC is assumed to be in thewrong location and orientation.

The system can determine the translation and orientation of the FMC atposition #2 by minimizing the discrepancy between the models across allfields in the region of overlap. For example, as shown in FIG. 7D, thesystem determines the translation and orientation needed to align thetwo models. Schematically, this shows the perfect agreement between thetwo field models when the correct second position is chosen for the FMC.

As shown in FIG. 8, the system generates a combined field model based onmodeled portions of the field (e.g., based on multiple local fieldmodels) by combining the multiple models to generate a combined fieldmodel. The system combines the multiple models based on the measuredsignals at each of the locations and the determined relative locationsof the FMC at each of the locations. More particularly, the fieldmapping catheter is moved around inside the organ of interest whileconstantly measuring the generated fields (or while measuring fields atpredefined time intervals or based on user selected times). The processof gathering signal measurements and aligning field models describedabove is repeated at several measurement locations. As shown in FIG. 8,the measurements from the multiple locations can be combined to generatea model of a larger portion of the field within the organ of interest.The signals measured at the multiple locations yields a set ofmeasurements and relative positions that can be combined to provide afield description for the entire volume of interest.

The FMC measurements at the multiple locations are combined to create afield map for each CIE pair over the entire region of interest. This“global” field map is used for tracking individual electrodes orcollections of electrodes. One method for generating the global fieldmap is to predict the potential at a given location by using the localfield generated by the nearest FMC measurement. This approach aligns andcombines all of the individual local field models. A second methodblends the local field models by weighted averaging depending upon theconfidence in each local field model at the given location. A thirdapproach is to generate a single field model using all of the FMCelectrode measurements and locations (either concurrently orsequentially).

As more data are collected, the additional data can be used to improvethe accuracy of the field map. The optimization used to find relativeFMC positions can incorporate knowledge about the number and quality ofthe measurements that predict potentials in the area. The field map canbe constructed, updated, and made more accurate as each new measurementbecomes available. When the field map is considered sufficientlyaccurate, a new FMC measurement position (or a position of anothermeasuring electrode on another catheter that is separate from the FMCcatheter) can be determined by comparing the new measurements with theglobal field map rather than a subset of the previous measurements.

Local Field Model

The physical laws governing an exemplary method of reconstruction of thefields in the vicinity of the FMC are briefly summarized below. If thecharge density at each point in a region of a homogeneous medium iszero, then the potential field satisfies Laplace's equation as shown inEquation1 1.

∇²φ=0   (1)

A field satisfying Laplace's equation over a volume is completelydetermined by the potential on a surface enclosing the volume.Furthermore, Laplace's equation is linear, so the potential at any pointwithin the volume is a linear combination (a weighted integral) of thesurface potentials.

The surface potential can generally be approximated using a finite setof discrete elements such that each element represents the potential ona small region of the surface. Using this approximation, the potentialat any point in the volume becomes a weighted sum of these surfacepotentials. Therefore, the potential at any set of points in the volumecan be represented by a matrix multiplication with the surfacepotentials, as shown in Equation 22.

Aφ_(s)=φ_(v)   (2)

Equation 22 states that a set of volume potentials, φ_(v), are eachcalculated as a linear combination of the finite set of surfacepotentials, φ_(s). The elements of the matrix A can be determined byvarious methods such as finite element method, finite difference method,boundary element method etc. The matrix A depends on the surfaceelements as well as the volume locations at which the potential is to becalculated.

FIG. 10 shows a flow chart of a method for generating a field map for anenclosed volume. At step 1002, the system collects field measurements atfield mapping points using the field mapping catheter. For example, asdescribed above, the FMC can be moved to different positions within theorgan and signals can be measured at each of the different positions.For a particular position (and associated set of signal measurements),at step 1004 the system defines a volume and an enclosing surface thatsurround the FMC. An exemplary volume and an enclosing surfacesurrounding the FMC is shown, for example, in FIG. 9. At step 1006, thesystem estimates the surface potentials (e.g., a potential distributionVs on the surface S), and therefore all of the enclosed volumepotentials, by solving Equation 22 for the surface potentials with theFMC electrode measurements as the given volume potentials. Determiningthe estimated surface potentials can include solving an inverse Laplaceproblem. Therefore, the FMC electrode locations and the enclosingsurface are used to find the values in the matrix A, and the measuredelectrode potentials are used for the volume potentials φ_(v).

In order to accurately represent the surface potential, the number ofsurface elements in φ_(s) tends to vastly exceed the number of FMCelectrode measurements in φ_(v). As a result, the problem isunderdetermined, implying that it has an infinite number of solutions. Aunique solution can be found by solving a least-squares problem thatincludes a term constraining the surface potentials, as shown inEquation 33.

$\begin{matrix}{{\hat{\phi}}_{s} = {\arg \; {\min\limits_{\phi_{s}}\left( {{{{A\; \phi_{s}} - \phi_{v}}}^{2} + {\alpha^{2}{{L\; \phi_{s}}}^{2}}} \right)}}} & (3)\end{matrix}$

There are two terms in this minimization. The first represents thesquared approximation error in satisfying Equation 22, which shouldideally be comparable with the expected measurement error. The secondterm represents the energy of a linear function of the surfacepotentials, and it is referred to as the regularization term.

If the matrix L in Equation 33 is diagonal, then the regularizationrepresents a weighted sum of the squared surface potentials, so theminimization balances the approximation error against the solutionenergy. Another option is to use a matrix L such that Lφ_(s) representsa weighted gradient of the surface potential. In that case, theminimization balances the approximation error against the variation ofthe potential across the surface. In either case, the regularizationfactor α controls the balance between the two error terms. The latterregularization scheme has been found to yield solutions that are smoothand yet accurate for a range of different regularization factors α. Aregularization factor of 0.01 is generally effective. Examples of theuse of Equation 33, as well as further details regarding the matrixcalculations, are described in patent application Ser. No. 11/451,898,entitled “NON-CONTACT CARDIAC MAPPING, INCLUDING MOVING CATHETER ANDMULTI-BEAT INTEGRATION” and filed Jun. 13, 2006, the contents of whichare incorporated by reference herein.

At step 1008, the system defines a field map function A as the forwardoperator from the surface distribution Vs to any point inside the volumeenclosed by surface S. More particularly, after calculating the surfacepotentials using Equation 33, it is possible to calculate the potentialat any point in the volume by applying Equation 22 for the givenlocation (the matrix A depends on the point being calculated). Thisprocess of estimating the surface potentials and then calculating volumepotentials is repeated for each generated field. This method generates afield map that is accurate for the entire enclosed volume.

It should be appreciated that similar methods can be used for generatingfield maps for different kinds of scalar or vector fields. An impedancefield can be generated using the same inverse approach to achieve anaccurate and differentiable impedance field map without interpolation.In the case where there are electrodes injecting currents inside thevolume, such as the case in which the field mapping catheter is involvedin the current injection, a similar inverse method can be used: insteadof using Laplace's equation, a more general representation of thepotential field, Poisson's equation, is used. Similar tools can be usedfor solving the inverse Poisson problem and generating a field map.

FMC Position Alignment

As described above, FMC measurements at the multiple locations (localfield maps) are combined to create a field map over the entire region ofinterest. This “global” field map is used for tracking individualelectrodes or collections of electrodes. In order to generate the globalfield map, the system determines relative positions of the FMC fordifferent signal measurements and combines multiple individual localfield models using the determined relative positions.

More particularly, in order to determine the relative positions of theFMC, the system solves an optimization problem to find the rotation andtranslation of a new FMC measurement relative to an existing field map.

Suppose that φ_(i)(r) is the existing model of the i^(th) field at thelocation r in the coordinate system of the field map. A new measurementwith the FMC provides an estimate of the fields at a discrete set ofpoints in the region around the FMC, and these estimates are denotedψ_(ij) for the i^(th) field and the j^(th) point. The locations of thesefield estimates are specified relative to the FMC itself rather than theexisting field map, and they are denoted p_(i). The corresponding pointsin the coordinate system of the field map depend on the rotation θ andtranslation t of the FMC and are denoted r_(j)(θ,t). The field estimatesψ_(ij) for the new measurement are therefore expected to match the fieldmap values φ_(i)(r_(j)(θ,t)) when the orientation θ and translation tare chosen correctly. We can solve for these parameters by minimizing asum of squared errors as shown in Equation 4 below.

$\begin{matrix}{\left( {\hat{\theta},\hat{t}} \right) = {\arg {\min\limits_{({\theta,t})}{\sum\limits_{i}\; {\sum\limits_{j}\; {w_{ij}{{{\phi_{i}\left( {r_{j}\left( {\theta,t} \right)} \right)} - \psi_{ij}}}^{2}}}}}}} & (4)\end{matrix}$

The sum of squared errors penalizes for differences in the fieldpredictions over a discrete set of points in the vicinity of the FMC. Itweights the penalty for the error at the j^(th) point in the i^(th)field by a weight w_(ij). These weights incorporate a priori and aposteriori knowledge of the measurement error, modeling error, andregion of valid overlap. For example, the modeling error is sensitive todistance from PMEs, so the weights may incorporate a term that isinversely proportional to the distance to the nearest electrode in theFMC. Any standard nonlinear optimization technique can be used to solveEquation 4 for the optimal parameters ({circumflex over (θ)},{circumflex over (t)}).

An alternative method for determining the relative positions of a set ofmeasurements is to create a common field model that predicts the fieldin a volume encompassing all of the measurements. For example, thecommon field can be modeled using the finite element method. The errorbetween the model and the measurements is then minimized to find therotation and translation of each FMC position. In this case, the modelφ_(i) of the i^(th) field depends on all of the assumed FMC electrodelocations and measured potentials, as shown below in Equation 5.

φ_(i)(r)=φ_(i)(r|{r _(j)(φ_(k) , t _(k))∀ j, k}, {ψ _(ijk) ∀ j, k})  (5)

Here, the new subscript k has been introduced to index each separate FMCmeasurement and position. Equation 5 shows that the field model atposition r depends on all of the FMC electrode locations and all of themeasured potentials.

If the k^(th) FMC measurement of the j^(th) electrode in the i^(th)field is denoted ψ_(ijk), and if the FMC electrode locations for thek^(th) measurement are denoted r_(j)(θ_(k), t_(k)) in the coordinatesystem of the field model, then the measurement positions can be foundby minimizing a sum of squared errors as shown in Equation 6 below.

$\begin{matrix}{\left( {{\hat{\theta}}_{1},{\hat{t}}_{1},\ldots \mspace{14mu},{\hat{\theta}}_{K},{\hat{t}}_{K}} \right) = {\arg {\min\limits_{({\theta_{1},t_{1},\ldots \mspace{14mu},\theta_{K},t_{K}})}{\sum\limits_{i}\; {\sum\limits_{j}\; {\sum\limits_{k}\; {{{\phi_{i}\left( {r_{j}\left( {\theta_{k},t_{k}} \right)} \right)} - \psi_{ijk}}}^{2}}}}}}} & (6)\end{matrix}$

This minimization is similar to Equation 4 except for the additionalmeasurements and the model dependency on all of the positions andmeasurements. It should be noted that the overall translation androtation of the field model is arbitrary. This is resolved in Equation 7by omitting from the minimization θ_(o) and t_(o), the positionalparameters of the first FMC measurement. These are assumed to be fixed,and they define the coordinate system of the field model. It should alsobe noted that Equation 8 can be modified to include weights as inEquation 4, and they can vary across field, electrode, and measurement.

Global Field Map Generation

The system can use various methods to generate the local field maps. Oneexemplary way to generate either a local field model or a global fieldmap is to generate a 3D grid with a resolution that fits the requiredaccuracy of the tracking system and then apply interpolation techniquesto the measured values. For example, the grid resolution may be 0.2 mm.An interpolation algorithm such as cubic interpolation can be used tointerpolate the measured values onto the grid.

An alternative method of generating the field model merges the localfield model from each successive FMC position into a continuallyimproving global field map on a grid spread throughout the volume ofinterest. Each local field model can be oriented with respect to thegrid on the region of interest, and it will provide predictions of thefield on the grid points contained within the local volume. The existingglobal field map values on the grid points have weights associated withthem, approximately representing the confidence attached to the fieldmap at each point. Similarly, the local volume predictions will havecompatible weights. The existing field map and the new local model canbe combined at each grid point using these weights, e.g., by using asimple weighted mean of the estimates as shown below in Equation 9.

$\begin{matrix}{{\phi (r)} = {\frac{1}{{w(r)} + {w_{local}(r)}}\left( {{{w(r)}{\phi (r)}} + {{w_{local}(r)}{\phi_{local}(r)}}} \right)}} & (9)\end{matrix}$

In Equation 9, φ(r) is the field map at the grid point r, φ_(local)(r)is the new local estimate of the field at the same point based on a newFMC measurement, w(r) is the weight associated with the existing fieldmap at r, and w_(local)(r) is the weight associated with the new localestimate at that point. The field map φ(r) is replaced with the weightedmean of the existing and new values. The weight w(r) must also beupdated to reflect the new information. One method for updating theweights is to simply add the new and old weights as shown in Equation10.

w(r)=w(r)+w _(local)(r)   (10)

The weights in this method can be taken to represent the inverse errorvariance of the field estimate at each point. For the local field model,the inverse error variance can be estimated using the local modelingerror and the expected error trends across the local volume, such thatthe error is assumed to be low near the PME electrodes and when themeasured potentials closely match the local model. The inverse errorvariance at the grid points of the field map can be initialized to zero(this assumes infinite initial error). It should be noted that thisprocess of updating the field model and weight must be repeated for eachfield (each CIE configuration).

Tracking

Once a set of expected signal measurements (e.g., a field map) has beenconstructed representing a region of interest, the field map can be usedto track electrodes and catheters within that region. The trackedelectrodes can be potential measuring electrodes on the FMC catheterand/or other potential measuring electrodes on different catheters.Using the field map, multiple electrodes (on one catheter or onmultiple, different catheters) can be tracked simultaneously.

PME tracking, which is described in more details below, is accomplishedby comparing PME measurements with expected signal measurements (e.g.,the measurements predicted by the field map) and then choosing the PMElocation that provides the best match. Catheter tracking, which is alsodescribed in more detail below, is accomplished similarly except thatPME locations are forced conform to the expected shape of the catheteron which they reside, or alternatively, the optimizer is penalized fordeviations from the expected shape constraints. PME and cathetertracking can be degraded by variations in field measurements withcardiac and respiratory cycle. Methods compensating for these variations(e.g., the variations due to cardiac and respiratory cycles) are alsodescribed below.

PME Tracking

Tracking of PME is performed by solving an optimization problem thatcompares the measurement collected by the PME as a result of activationof the CIE pairs to expected measurements in the field map in a givenlocation. The electrode is assigned the location that in some wayminimizes the error between the expected field in the field map and themeasured field. The following describes one exemplary method fordetermining the location of the tracked PME. However, other methods arepossible.

FIG. 11 shows an exemplary flow chart of a process for determiningpositions of PME using a field map (e.g., a field map generated usingone or more of the methods described herein).

At step 1102, the system obtains a field map. The field map assignsfield measurements to each location in space and can be generated usingone or more of the methods described herein.

At step 1104, CIE are positioned in the cavity (these CIE are the sameCIE used to generate the field map). At step 1106, the system causes theCIE to inject current using each of the CIE configurations used togenerate the field map. For example, in the case of three CIE pairs,each location in 3D space r=(x,y,z) is assigned three measurements,φ₁(r), φ₂(r), and φ₃(r), corresponding to the three different fieldsgenerated by the CIE pairs. At step 1108, signals are measured on thePME on catheters positioned in the organ (e.g., the tracked catheters).In the example with three CIE pairs, three measured potentials, v₁, v₂,and v₂, are obtained from the tracked PME: one for each CIE pair. Basedon the measured signals and the field map, at step 1110, the systemdetermines positions for each of the PME by solving an optimizationproblem that compares the measured signals with the values of theexpected signals in the field map. Accordingly, the PME can be assignedthe location, {circumflex over (r)}=({circumflex over (x)},ŷ,{circumflexover (z)}), that minimizes the sum of squared measurement errors asshown in Equation 11.

$\begin{matrix}{\hat{r} = {\underset{r}{argmin}{\sum\limits_{i}\; {{{\phi_{i}(r)} - v_{i}}}^{2}}}} & (11)\end{matrix}$

Equation 11 is a nonlinear optimization problem, and it can be solvedusing an iterative scheme such as Newton-Raphson or Levenberg-Marquardtor a direct search method such as the Nelder-Mead Simplex Method. Theoptimization in Equation 11 determines the location of PME without anyprior knowledge of the CIE spatial configuration or any prior knowledgeof the characteristics of the medium. In the case of more than threepairs of CIEs, the solution for {circumflex over (r)} becomesover-determined since we obtain more equations than unknowns, which mayhelp improve tracking accuracy depending on the specific embodiment.

The optimization in Equation 11 can be modified in several ways toadjust the behavior of the tracking algorithm. A weighting factor can beapplied to the error in each field, which can be used, for example, toprevent the solution being dominated by the contribution of the nearestCIE. The sensitivity of the optimization to each field error can also beadjusted by replacing the sum of squares with a sum of errors raised toa different power; for example, raising error to the fourth power makesthe optimization more sensitive to the largest error among the fields,whereas summing the absolute value of each error makes the optimizationless sensitive to the worst field error. Another option is to use asorting filter, such as a weighted median or maximum, in place of thesum of squares. Using a sorting filter also adjusts the sensitivity ofthe optimization to outlying errors.

It should be appreciated that more than one PME may be trackedsimultaneously using this scheme. To do so, signals are acquired fromand an optimization problem is solved for each of the electrodes beingtracked. If such electrodes are mounted on different catheters, then itis possible to simultaneously track multiple catheters.

The measurements collected at the PMEs as a result of current injectedby the CIE are generally affected by the complex conductivity, oradmittivity, distribution of the medium. It should be noted that theoptimization in Equation 11 is valid for either real- or complex-valuedmeasurements. As a result, both amplitude and phase may be used fortracking purposes. Use of the imaginary part of the complex conductivityis of particular importance in material distributions where thepermittivity contrast exceeds that of the conductivity contrast.

Catheter Tracking

By tracking the individual PME on a catheter, the location and shape ofthe catheter can be determined. Also, because measurements from multiplePME are used to track the catheter, tracking accuracy can be improvedover what is possible with a single PME. PME can be constrained by thecatheter in several ways as described below.

If the electrodes are constrained in such a way that they cannot moverelative to each other, then the catheter is considered a rigid body,and only the translation and rotation of this body must be determined byoptimization. The catheter position can be found by minimizing a sum ofsquared errors as in Equation 11 except that (1) the errors are summedover all PME and (2) the PME locations are determined by translating androtating a set of reference locations representing the positions of thePME on the catheter. The optimization then finds the cathetertranslation and rotation that minimize the error over all PME, and thisgives the position of the region of the catheter where the PME arelocated. (The shape of the catheter is fixed and known.) As in the caseof individual PME, the optimization in Equation 11 can be modified byweighting the errors from each field and each PME or by replacing thesum of squared errors with a different, possibly nonlinear, combinationof errors.

If the electrodes are constrained such that their spacing cannot change,then inverse kinematics can be used to solve for their positions.Inverse kinematics solves for the joint angles of a chain of jointsconnected by rigid segments. As before, some combination of errors overall fields and all PME can be minimized to find the PME locations, butat each step in the optimization, the locations of the PME areconstrained to maintain the segment lengths. The optimization finds theposition of each PME, giving the shape and position of the region of thecatheter where the PME are located. The kinematic model assumes that thecatheter forms a straight line segment between each pair of PME, butinterpolation methods can be applied in order to find a more realisticshape for the catheter.

The PME tracking problem in Equation 11 can be augmented with penaltiesfor incorrect catheter shape. For example, a second error term can beadded to Equation 11 that quantifies the difference between thepredicted electrode spacing and the expected spacing. By adjusting therelative weight applied to this second error term, the balance betweenmeasurement error and spacing error can be adjusted in the optimization.As another example, the PME can be taken to lie on a flexible beam, andthe predicted beam stress or loading can be used as an additional errorterm in Equation 11. These methods do not directly result in a shape forthe catheter, but interpolation methods can be used to solve for thecomplete catheter shape.

Another exemplary method for tracking a catheter is to solve for thelocations of each of the PME and then fit them onto a model of thecatheter. For example, if the catheter is taken to be a rigid body, thenthe catheter translation and rotation can be found that minimize thedistance between the PME on the rigid body and the optimized PMElocations. As another example, the shape of a kinematic chain can befound such that the distance between the joints and the optimized PMElocations is minimized.

Cardiac and Respiratory Motion

Cardiac contraction and respiration change the medium in which thefields are being generated, thus changing the generated fields. In otherwords, the actual fields are time-varying. There are several ways toaddress this issue.

One approach is to apply a low-pass filter to the measured potentials inorder to reduce measurement variation due to cardiac and respiratorycycles. For example, a filter that only passes signals below thefundamental frequency of the respiratory and cardiac cycles will removetheir effects.

A second approach is to generate separate field maps for various phasesin the cardiac and respiratory cycle: this is called phase-gating. Inthis case, a PME is tracked by optimizing its location in a field mapcorresponding to the current cardiac and/or respiratory cycle phase. Thecycle phase is detected using measurements from PME on stationarycatheters, such as those on which the CIE reside, and/or cutaneouspatches such as ECG. The variation in these stationary measurements isdue to cardiac and respiratory cycle. By comparing the currentstationary PME measurements with previous measurements corresponding toeach phase, the current phase can be determined. Templates or exemplarsfor each phase can be picked by various clustering methods such as, forexample, k-means clustering.

A third approach is to normalize the data for the field variation due tocardiac and respiratory cycle. A substantial part of the field variationis additive and is common to all measurements in the region of interest.It is possible to synthesize this additive component using measurementsfrom a set of PME on stationary catheters (e.g. where the CIE reside)and then subtract it from the measured potentials. The additive phasevariation is thereby removed from the measurements.

The additive phase-dependent field variation can be synthesized asfollows. When the FMC is in a stationary position, the variation in itsmeasurements is largely due to cardiac and respiratory cycle. With theFMC in a stationary position in the region of interest, the meanmeasurement across the electrodes on the FMC (the FMC common mode) iscalculated, and then the mean across time is subtracted from it. Theresulting signal represents the expected phase-dependent field variationfor FMC measurements in the region of interest. This variation can beapproximately synthesized as a linear combination of the PMEmeasurements on stationary catheters. The mean across time is subtractedfrom each stationary PME measurement, and the result represents thephase-dependent field variation detected by each stationary PME. Thelinear combination of PME measurements is selected such that thecombination of PME phase-dependent field variations best matches thephase-dependent field variation measured by the FMC.

One specific method for determining the desired linear combination ofstationary PME measurements is described below. As shown in Equation 12,a linear least-squares problem can be solved to find the weights thatshould be applied to the stationary PME measurements such that their sumbest approximates the expected phase-dependent field variation on theFMC.

φ_(CM) −E{φ _(CM)}=[φ_(S1)}φ_(S2) −E{φ _(S2)} . . . ]·α  (12)

In the above: φ_(CM) is the mean across the FMC electrodes (commonmode); E{·} is the mean over time; φ_(S1) is the measurement from thefirst stationary PME; and α is the set of weights applied to eachstationary PME measurement. This linear equation is solved for theweights α using least squares, and the resulting weights are used tosynthesize the additive phase variation component. The above proceduremust be repeated for each field.

There are several related ways to solve for the set of weights appliedto the stationary PME measurements in order to synthesize the additivephase-dependent field variation. Rather than only solving usingmeasurements in one stationary FMC position, the weights can be foundthat optimize for multiple stationary FMC positions by verticallyconcatenating the corresponding measurements in Equation 12 and solvingfor a single set of weights. Also, rather than solving a linearleast-squares problem for the weights, a more general optimizationapproach can be used to solve for the weights. For example, standardoptimization techniques can be used to find weights that are nonnegativeor that sum to 1.

An additive correction for phase-dependent field variation onlycompensates for an overall offset in the field, but it is possible tocompensate for higher-order variations in each field due to cardiac andrespiratory cycle. For example, a phase-dependent scaling term can beused to compensate for changes in field strength with cardiac andrespiratory cycle. Such a scaling term can be determined by collectingFMC measurements in a set of stationary locations and then optimizingfor a combination of stationary PME measurements that best approximatesthe phase-dependent field strength variation.

FGD Displacement Correction

As described above, PME are tracked based on a comparison between a setof expected signals (e.g., a field map) and a signal measured on a PMEof a tracked electrode where the CIE used to generate the signals forobtaining the field map and for tracking the PME are the same (and arein the same locations). In order to correctly determine the position oftracked electrodes, the CIE should be kept in the same location as theywere in when the field map was generated. However, during field mappingor catheter tracking, the FGD may become unintentionally displaced. Forexample, if several CIE reside on a catheter in the coronary sinus, acatheter moving in the right atrium may come into contact with thecoronary sinus catheter and displace it. The catheter carrying the FGDmay also be displaced due to patient respiration or other patientmovement. One approach to overcoming this issue is the use of a deviceor method to keep the FGD carrying catheter stably positioned. This canbe accomplished by using any of a number of fixation schemes, forexample scaffolding or a balloon anchor. Another approach is a subsystemthat can detect such displacement and aid the user in correcting it.This can be accomplished in several ways as described below.

FGD displacement correction involves the detection of relativedisplacement between FGD and one or more PME that are known to be in astable position. Cutaneous PME or stable intracardiac PME can be used tocollect stable measurements for this purpose. In particular, standardECG leads, which are PME, can be used for the dual purpose of measuringcardiac electrical activity and monitoring tracking signals using themultiplexing scheme described earlier. Furthermore, additional cutaneousPME can be used to increase the accuracy of the displacement correctionsubsystem.

With the FGD in an initial position, stable PME can be used to form abaseline measurement of the generated fields (for example, the systemcan cause current to flow among the current injecting electrodes andmeasure signals at measuring electrodes positioned at one or more securelocations). Measurements from the stable PME (e.g., signals measured atthe PME in response to current flow from the current injectionelectrodes) are then monitored and compared to the baseline measurementsto detect changes due to displacement of the FDG. The error between thebaseline and the current measurements can be quantified using a distancemetric, such as the L2 norm, and displacement can then be detected bycomparing the error metric with a threshold value. If the error metricexceeds the preset threshold, the clinician is alerted that the FGD hasbeen displaced.

In addition to alerting the clinician, the error metric can be used toguide the catheter back to the initial position. As the clinician movesthe displaced FGD, the value of the error metric is displayed andupdated. When the error metric falls under the preset threshold, anindication is provided that the FGD has returned to the initialposition.

Furthermore, the signals collected by the stable PME can be used toguide the catheter back to the initial position by approximatelytracking the FGD in 3D space. FGD tracking can be accomplished in anumber of ways, several of which are outlined below.

As in the case of PME tracking, FGD tracking requires a model of thegenerated fields—the equivalent of a field map. The fields generated bythe FGD are modeled in the vicinity of the stable PME. PME measurementscan be tracked in this field model to determine the displacement of thegenerated fields and thus the displacement of the FGD. Inaccuracies inthe field model will cause the detected displacement to be distorted,but it can still provide useful information to the clinician or to thetracking algorithm.

For example, a three-dimensional polynomial model can be fit to theinitial measured data if the approximate locations of the stable PME areknown. It is then assumed that the field model moves with the FGD, andtherefore any change in the stable PME measurements relative to thefield model is indicative of FGD movement. Displacement of the FGD cantherefore be quantified by tracking the PME measurements as a rigid bodywithin the field model using rigid body catheter tracking techniquesdescribed in the previous section.

Rather than modeling the field in the vicinity of the stable PME usingthe initial measurements and then tracking subsequent PME measurementswithin this model, other approaches can be used to determine the FGDdisplacement. For example, a field model can be constructed for eachmeasurement, and then the rigid body motion can be determined thatprovides the best match between the two models in the region of the PME.As another example, a single field model can be constructed that bestmatches both the initial measurement and the current measurement suchthat the two measurements are related by a rigid body motion.

Other mathematical methods can be used to model the fields for FGDtracking. For example, rather than modeling each field as a polynomial,the CIE generating each field can be modeled as electric monopoles in ahomogeneous medium. Given a set of stable PME measurements and theirapproximate locations, the monopole locations (and thus CIE locations)and monopole strengths can be determined that best match the measuredpotentials. This field modeling approach is similar to the polynomialfield modeling approach, but it has the benefit that each field modeldefines the CIE locations, whereas the polynomial field model only givesthe relative displacement of the entire field. As before, inaccuraciesin the field model will distort the tracked FGD locations, but thetracked positions can still provide useful information to the clinician.

If the stable PME locations are unknown but the initial CIE locationsare known, for example, based on the field map constructed for PMEtracking, an electric monopole model can be used to determine thelocations of the stable PME measurements, and subsequent stable PMEmeasurements can be used to track displacement of the CIE. In this way,all of the spatial information required for both PME tracking and FGDtracking can be derived from the shape of the FMC and the measurementscollected from the available PME.

When different fields are generated by some of the same CIE, or whendifferent CIE on the same FGD are used, FGD tracking can be constrainedusing this information. For example, if each field is generated by adifferent CIE on the same FGD, and if each CIE is modeled as an electricmonopole as described above, the optimization used to find the monopolelocations can be constrained such that the monopoles obey knowninter-electrode spacing on the shared FGD. This will yield more a morerealistic FGD shape and can make the FGD tracking more robust. Othercatheter shape constraints, such as a rigid catheter shape, can be usedto improve CIE and FGD tracking

Cardiac and respiratory motion will cause the FGD to move relative tothe fixed PME and will also distort the PME measurements. Thisphase-dependent measurement variation can be compensated using themethods described in the previous section for compensating tracked PMEmeasurements.

Experimental Results

Field mapping, electrode tracking, and FGD tracking have beendemonstrated ex vivo using measurements collected in a nine-liter salinetank. The field mapping and electrode tracking results reported belowwere collected using two commercially-available decapolar catheters asFGD, a multielectrode array catheter as described in application Ser.No. 12/005,975 as the FMC, and a commercially-available decapolarcatheter as the tracked catheter.

FIG. 12 shows a table of experimental results. The table includescontour plots of two-dimensional slices of the local model and globalfield map as new measurements are aligned and combined with the existingfield map for one field.

In the experimental results shown in FIG. 12, the FMC was manually movedwithin the saline, and the FMC measurements collected in eight fieldswere used to construct a global field map using the methods describedabove in Equations 4, 9, and 10. Contour plots of two-dimensional slicesof one of the eight fields of the local model and the global field mapare used in FIG. 12 to show how each is generated with sequential FMCmeasurements. Each row shows the new local model, the existing globalfield map, and the updated field map for a new FMC measurement. In thefirst column, the FMC electrodes are shown superimposed on the localmodel generated from the new measurement. In the third column, thepositions of the FMC electrodes after alignment are shown superimposedon the new global field map following the update. Each new local modelslightly modifies and expands the global field map in the region aroundthe FMC.

The field map constructed as shown in FIG. 12 was used to track PME on acommercially-available decapolar catheter using potential measurementscollected from the PME in the saline tank with the tracking methoddescribed in Equation 11. Three-dimensional tracked PME locations areshown from two views in FIG. 13 for four different catheter positions.For clarity, tracked locations for only five of the PME are plotted, andthey are connected with lines to show the shape of the decapolarcatheter. The physical spacing between the tracked PME is 9 mm, so thetotal length of the tracked section of the catheter is 36 mm.

Other Embodiments

The methods and systems described herein are not limited to a particularhardware or software configuration, and may find applicability in manycomputing or processing environments. The methods and systems can beimplemented in hardware, or a combination of hardware and software,and/or can be implemented from commercially available modulesapplications and devices. Where the implementation of the systems andmethods described herein is at least partly based on use ofmicroprocessors, the methods and systems can be implemented in one ormore computer programs, where a computer program can be understood toinclude one or more processor executable instructions. The computerprogram(s) can execute on one or more programmable processors, and canbe stored on one or more storage medium readable by the processor(including volatile and non-volatile memory and/or storage elements),one or more input devices, and/or one or more output devices. Theprocessor thus can access one or more input devices to obtain inputdata, and can access one or more output devices to communicate outputdata. The input and/or output devices can include one or more of thefollowing: Random Access Memory (RAM), Redundant Array of IndependentDisks (RAID), floppy drive, CD, DVD, magnetic disk, internal hard drive,external hard drive, memory stick, or other storage device capable ofbeing accessed by a processor as provided herein, where suchaforementioned examples are not exhaustive, and are for illustration andnot limitation.

The computer program(s) can be implemented using one or more high levelprocedural or object-oriented programming languages to communicate witha computer system; however, the program(s) can be implemented inassembly or machine language, if desired. The language can be compiledor interpreted. The device(s) or computer systems that integrate withthe processor(s) can include, for example, a personal computer(s),workstation (e.g., Sun, HP), personal digital assistant (PDA), handhelddevice such as cellular telephone, laptop, handheld, or another devicecapable of being integrated with a processor(s) that can operate asprovided herein. Accordingly, the devices provided herein are notexhaustive and are provided for illustration and not limitation.

References to “a microprocessor” and “a processor”, or “themicroprocessor” and “the processor,” can be understood to include one ormore microprocessors that can communicate in a stand-alone and/or adistributed environment(s), and can thus be configured to communicatevia wired or wireless communications with other processors, where suchone or more processor can be configured to operate on one or moreprocessor-controlled devices that can be similar or different devices.Furthermore, references to memory, unless otherwise specified, caninclude one or more processor-readable and accessible memory elementsand/or components that can be internal to the processor-controlleddevice, external to the processor-controlled device, and can be accessedvia a wired or wireless network using a variety of communicationsprotocols, and unless otherwise specified, can be arranged to include acombination of external and internal memory devices, where such memorycan be contiguous and/or partitioned based on the application.Accordingly, references to a database can be understood to include oneor more memory associations, where such references can includecommercially available database products (e.g., SQL, Informix, Oracle)and also proprietary databases, and may also include other structuresfor associating memory such as links, queues, graphs, trees, with suchstructures provided for illustration and not limitation.

Accordingly, other embodiments are within the scope of the followingclaims.

1.-34. (canceled)
 35. A system comprising: a catheter configured forinsertion into an organ in a patient's body and comprising multiplemeasuring electrodes; multiple current injecting electrodes placed instable locations inside a patient's body to generate a field in anorgan; an electronic control system coupled to the multiple currentinjecting electrodes and to the measuring electrodes and configured to:cause current to flow among multiple current injecting electrodes togenerate a field in an organ and to measure the field; in response tothe current flow caused by the current injecting electrodes, measure asignal at each of the multiple measuring electrodes for each of multiplelocations of the catheter; a processing system coupled to the electronicsystem and configured to: determine expected signals at additionallocations within the organ based on the measured signals; and determinea position of at least one of the measuring electrodes of the catheterand/or a measuring electrode of another catheter in the organ based onat least the expected signals.
 36. The system of 35, wherein the currentinjecting electrodes are mounted on one or more catheters that aresecured inside the organ.
 37. The system of 35, wherein the measuringelectrodes mounted on the catheter comprise electrodes that can be movedand positioned at multiple locations in an organ.
 38. The system ofclaim 35, wherein the current-injecting electrodes comprise at leastthree sets of current injecting electrodes.
 39. The system of 35,wherein the current injecting electrodes are not on the catheter thatincludes the measuring electrodes.
 40. The system of 35, wherein theprocessing system is further configured to determine the expectedsignals in the absence of information from an external tracking system.41. The system of 35, wherein the processing system is furtherconfigured to determine relative locations of the plurality of measuringelectrodes at different ones of the multiple locations in the organbased on the measured signals.
 42. The system of 41, wherein theprocessing system is further configured to reconcile fields measured atthe different ones of the multiple locations using a cost minimizationfunction.
 43. The system of 35, wherein the processing system is furtherconfigured to determine a translation and rotation between the pluralityof measuring electrodes at the multiple locations.
 44. The system of 35,wherein the measured signals for the catheter at each location define acorresponding set of measurements and wherein the processing system isfurther configured determine the expected signals by combininginformation from the different sets to determine a field map indicativeof the expected signals at the additional locations.
 45. The method ofclaim 44, wherein the processing system is further configured to combinethe information from the different sets to determine a field map byaligning the information from the different sets to account for thedifferent locations of the catheter based on the known relativelocations of the measuring electrodes on the catheter.
 46. The system of35, wherein the expected signals comprise a field map.
 47. The system of35, wherein the processing system is further configured to determine theexpected signals using Laplace's equation.
 48. The system of 35, whereinthe processing system is further configured to determine the expectedsignals using Poisson's equation.
 49. The system of 35, wherein theprocessing system is further configured to determine the expectedsignals using a polynomial estimation.
 50. The system of 35, wherein thecurrent injecting electrodes comprise both electrodes mounted on one ormore catheters secured inside the organ and one or more body-surfaceelectrodes.
 51. The system of 35, wherein the processing system isfurther configured to use the expected signal measurements to track alocation of the measuring electrode of the another catheter.
 52. Thesystem of 35, wherein the processing system is further configured toprocess the measured signals and expected signals to account forrespiration and heart beat.